What’s that all about the contrasts

Hi Wolfgang and Michel, here is a simple example to show the differences between treatment and effect contrast.

Example dataset

Create a random dataset with criteria y, predictors x1 and x2 and gender.

All variables are correlated.

n <- 10000
gender <- rep(0:1, each = n/2)
y <- sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x1 <- y + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)
x2 <- y + x1 + sample(0:10, n, replace = TRUE) + gender * sample(0:10, n, replace = TRUE)

dat <- data.frame(y = y, x1 = x1, x2 = x2, gender = gender)

Descriptives

psych::corr.test(dat)

Call:psych::corr.test(x = dat)
Correlation matrix 
          y   x1   x2 gender
y      1.00 0.80 0.86   0.54
x1     0.80 1.00 0.93   0.67
x2     0.86 0.93 1.00   0.73
gender 0.54 0.67 0.73   1.00
Sample Size 
[1] 10000
Probability values (Entries above the diagonal are adjusted for multiple tests.) 
       y x1 x2 gender
y      0  0  0      0
x1     0  0  0      0
x2     0  0  0      0
gender 0  0  0      0

 To see confidence intervals of the correlations, print with the short=FALSE option

psych::describe(dat)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
y	1	10000	7.4457	4.589897	7.0	7.216625	4.4478	0	20	20	0.3883082	-0.3977414	0.0458990
x1	2	10000	14.9664	7.384858	14.0	14.643500	7.4130	0	39	39	0.3800873	-0.4494918	0.0738486
x2	3	10000	29.8458	13.730130	28.0	29.279875	14.8260	0	73	73	0.3560139	-0.5703444	0.1373013
gender	4	10000	0.5000	0.500025	0.5	0.500000	0.7413	0	1	1	0.0000000	-2.0002000	0.0050003

Contrasts

The left part of the table is with gender as treatment contrast (0 vs. 1) and the right part with gender as effect contrast (-1 vs. 1)

# Gender has values 0 vs. 1 (treatment contrast)
fit1 <- lm(y ~ gender * x1 * x2, data = dat)

# Gender hast -1 vs. 1 (effect contrast)
dat$gender <- car::recode(dat$gender, "0 = -1; 1 = 1")

fit2 <- lm(y ~ gender * x1 * x2, data = dat)

sjPlot::tab_model(fit1, fit2, show.std = TRUE, show.ci = FALSE, col.order = c("est", "se", "std.est", "p"), digits = 4)

	y			y
Predictors	Estimates	std. Beta	p	Estimates	std. Beta	p
(Intercept)	-1.7305	0.0063	<0.001	-2.4594	0.0063	<0.001
gender	-1.4577	-0.1888	<0.001	-0.7288	-0.1888	<0.001
x1	0.0024	-0.0019	0.913	-0.0027	-0.0019	0.848
x2	0.3366	0.9998	<0.001	0.3334	0.9998	<0.001
gender × x1	-0.0103	-0.0047	0.720	-0.0051	-0.0047	0.720
gender × x2	-0.0063	-0.0061	0.679	-0.0031	-0.0061	0.679
x1 × x2	-0.0000	0.0011	0.979	0.0001	0.0011	0.909
(gender × x1) × x2	0.0001	0.0016	0.872	0.0001	0.0016	0.872
Observations	10000			10000
R2 / R2 adjusted	0.759 / 0.759			0.759 / 0.759